Preamble

Synchrotron emission is gyromagnetic emission from ultrarelativistic particles. It is important in the laboratory as a source of radiation in synchrotrons and as an energy loss mechanism for relativistic electrons confined by a magnetic field. Synchrotron radiation is of particular importance in astrophysics because it is the dominant emission mechanism for the vast majority of radioastronomical sources.

Forward Emission by Relativistic Particles

Before discussing synchrotron emission in particular, it is appropriate to discuss emission by relativistic particles in general. Important features of the emission by relativistic particles may be determined by the special theory of relativity and are only weakly dependent on the specific emission mechanism involved. Emission by a particle which is highly relativistic in the laboratory frame K may be inferred from its emission pattern in its rest frame K0. Let the instantaneous velocity v of the particle in K be along the z axis. The frame K0, as viewed from K is moving along the z axis at velocity v, as illustrated in Figure 24.1, and the frame K, as viewed from K0, is moving along the z0 axis at velocity –v.

In K0 the particle is momentarily at rest, and so its emission pattern is dipolar. For present purposes the only important point is that the emission pattern in K0 is not highly anisotropic. Let w0, k0, ψ0 describe a plane wave in K0, with ψ0 the angle between k0 and the z0 axis.